An opinion dynamics approach to model and analyze the behavior of consumers in an energy network

Motivated by theories and evidence from the social psychology literature, we propose a novel continuous-time mathematical model that captures the evolution of motivation and behavior of energy consumers in a social network. In our model, consumers are connected to the energy grid and their energy demand (which we shall refer to as their behavior) is affected by their personal motivation on reducing (or increasing) their energy consumption. The motivation-behavior dynamics of each consumer is modeled using a second-order continuous-time bilinear differential equation. Each consumer has the ability to share their motivation on a social network and observe the behavior of other consumers. Using the information gathered from their peers and their personal bias about the energy consumption behavior, consumers have the ability to revise their own motivation about energy consumption and, ultimately, their behavior. Moreover, we incorporate into the model an external control action that captures the implementation of external behavioral interventions that influence the weight each consumer assigns to their own bias. Then, we use the proposed framework to shed light on the collective motivation-behavior dynamics of all the consumers, establishing conditions for the existence of equilibria, characterizing them, and performing a sensitivity analysis of such equilibria with respect to variations in the steady-state interventions provided to each consumer.